- Nov 24, 2007
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I'm trying to figure out a formula for the number of possible combinations for a group of 20 objects. This is NOT a question about permutations. Each object can only occur once, but also, they can only occur in a particular order.
There would be no reorganizing them to produce different combinations.
So that means that if all the objects are present, there's only one possible combination. If they were represented by letters:
(obviously)
With only one possible object, there are 20 different versions.
(again, obviously)
With two possible objects:
Now, once we get to three objects, that's where I start to lose it. It seems like it would be as above, only starting with "ABC ABD ABE ABF..." then repeating again, without the A: "BCD BCE BCF BCG..."
Then again, without the B: "CDE CDF CDG CDH..."
And so on. It would have to be repeated a total of 18 times, until the last possible combination of RST.
Then when you get to four objects, I THINK it would have to be repeated 18*17 times. Is that correct? If so, then with five objects, it would have to be repeated 17*16, then with six, 16*15.
But I'm just guessing.
Any help?
There would be no reorganizing them to produce different combinations.
So that means that if all the objects are present, there's only one possible combination. If they were represented by letters:
Code:
ABCDEFGHIJKLMNOPQRST
With only one possible object, there are 20 different versions.
Code:
A B C D E F G H I J K L M N O P Q R S T
With two possible objects:
Code:
AB AC AD AE AF AG AH AI AJ AK AL AM AN AO AP AQ AR AS AT
BC BD BE BF BG BH BI BJ BK BL BM BN BO BP BQ BR BS BT
CD CE CF CG CH CI CJ CK CL CM CN CO CP CQ CR CS CT
DE DF DG DH DI DJ DK DL DM DN DO DP DQ DR DS DT
EF EG EH EI EJ EK EL EM EN EO EP EQ ER ES ET
FG FH FI FJ FK FL FM FN FO FP FQ FR FS FT
GH GI GJ GK GL GM GN GO GP GQ GR GS GT
HI HJ HK HL HM HN HO HP HQ HR HS HT
IJ IK IL IM IN IO IP IQ IR IS IT
JK JL JM JN JO JP JQ JR JS JT
KL KM KN KO KP KQ KR KS KT
LM LN LO LP LQ LR LS LT
MN MO MP MQ MR MS MT
NO NP NQ NR NS NT
OP OQ OR OS OT
PQ PR PS PT
QR QS QT
RS RT
ST
Then again, without the B: "CDE CDF CDG CDH..."
And so on. It would have to be repeated a total of 18 times, until the last possible combination of RST.
Then when you get to four objects, I THINK it would have to be repeated 18*17 times. Is that correct? If so, then with five objects, it would have to be repeated 17*16, then with six, 16*15.
But I'm just guessing.
Any help?
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